For my math project, I am working on creating a visualization tool for a linear regression plane. I have completed the mathematical aspects of the project, but I am unsure of how to graph the plane. The equation I am working with is z=C+xD+yE, where C, D, and E are constants that are already known. Can anyone provide guidance on how to graph this plane using this information? Thank you.
Check out my GitHub page:
z=C+xD+yE
The equation provided contains all the necessary information to define the plane. Additional tools may be required depending on the graphic software being used. The canonical form of the equation is:
xD + yE - z + C = 0
The normal vector to the plane is (D, E, -1) with a distance from the origin given by Abs(C)/Sqrt(D^2+E^2+1).
The plane intersects the coordinate axes at points (-C/D), (-C/E), (C)
Your struggle seems to lie not in math, but in dealing with the concept of three, as noted by WestLangley in his comment, you have the option to experiment with rotations or even construct a basic triangle which is the simplest approach
If you already have the equation for the plane, create 3 points to establish a triangle
// z=C+xD+yE
// I am assuming that the plane is not aligned with any axis
// and does not pass through the origin; otherwise, choose points differently
var point1 = new THREE.Vector3(-C/D,0,0);// intersecting point on x-axis
var point2 = new THREE.Vector3(0,-C/E,0);// intersecting point on y-axis
var point3 = new THREE.Vector3(0,0,C);// intersecting point on z-axis
Next, construct a new geometry as shown in How to make a custom triangle in three.js
var geom = new THREE.Geometry();
geom.vertices.push(point1);// adding vertices to geometry
geom.vertices.push(point2);
geom.vertices.push(point3);
// specifying that vertices 0,1,2 form a face = triangle
geom.faces.push( new THREE.Face3( 0, 1, 2 ) );
Create a simple material and incorporate it into a scene
var material = new THREE.MeshBasicMaterial({
color: 0xff0000, // RGB hex color for material
side: THREE.DoubleSide // prevent object from being hidden when viewed from behind
});
scene.add(new THREE.Mesh(geometry,material));
This should set you on the right path; feel free to add more triangles or expand its size by selecting points further apart
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